Pivotality, twisted centres, and the anti-double of a Hopf monad

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

Finite-dimensional Hopf algebras admit a correspondence between so-called pairs in involution, one-dimensional anti-Yetter--Drinfeld modules and algebra isomorphisms between the Drinfeld and anti-Drinfeld double. We extend it to general rigid monoidal categories and provide a monadic interpretation under the assumption that certain coends exist. Hereto we construct and study the anti-Drinfeld double of a Hopf monad. As an application the connection with the pivotality of Drinfeld centres and their underlying categories is discussed.

Details

OriginalspracheEnglisch
Seiten (von - bis)86–149
Seitenumfang64
Fachzeitschrift Theory and applications of categories : TAC
Jahrgang41
Ausgabenummer4
PublikationsstatusVeröffentlicht - 2024
Peer-Review-StatusJa

Externe IDs

Scopus 85184419811

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

  • math.QA, math.CT, primary:18M15, secondary: 16T05, 18C20, 18M30, anti-Drinfeld double, comodule monads, Pivotal categories, Hopf monads, centres, heaps, module categories